Do you agree with the link that you provided claiming that "a controversial paper exists but so do black holes"? It sure sounds like you do. In my experience most physicists would make the same statement...until they are pressed to define the term "exists"...which will eventually lead them to conclude that the word itself is not compatible with the theory of general relativity (or something along those lines). Science can't have it both ways, claiming colloquially that black holes as predicted by GR exist as a matter of fact, and also that the word "exists" has no real place in the theory of GR. By the way, I can personally provide a definition of "exists" which is perfectly compatible with GR but would lead to the conclusion that black holes do not qualify.